UNIVERSITY  OF  CALIFORNIA  PUBLICATIONS 

IN 

AGRICULTURAL    SCIENCES 

Vol.  4,  No.  5,  pp.  121-139,  1  text  figure  May  10,  1919 


VAEIABILITY  IN  SOILS  AND  ITS  SIGNIFICANCE 
TO  PAST  AND   FUTURE   SOIL 
INVESTIGATIONS 

II.    VARIATIONS    IN   NITROGEN   AND    CARBON   IN    FIELD 

SOILS  AND  THEIR  RELATION  TO  THE  ACCURACY 

OF  FIELD  TRIALS 

BY 

D.  D.  WAYNICK  and  L.  T.  SHAEP 


Introduction 

Investigations  carried  out  under  field  conditions  are  subject  to  a 
number  of  variables,  all,  or  any  one  of  which  may  serve  to  invalidate 
the  results  which  may  be  secured.  The  problem  of  adequate  experi- 
mental control  is  an  exceedingly  difficult  one,  and  unlike  many 
experiments  carried  out  in  the  laboratory  none  of  the  variables  met 
with  in  the  field  are  capable  of  complete  elimination.  They  may, 
however,  be  allowed  for,  at  least  in  so  far  as  they  are  concerned  with 
the  soil  mass,  if  we  know  the  magnitude  of  the  variables  met  with. 
The  heterogeneity  of  the  soil,  even  in  experimental  plots,  has  been 
quite  generally  recognized  as  a  factor  which  may  render  the  data 
secured  from  field  plots  open  to  more  or  less  serious  errors;  but  that 
the  soil  may  be  so  variable  as  to  render  the  measurements  made  of 
soil  constituents  of  very  questionable  value  has  not  been  fully  appreci- 
ated. There  are  considerable  data,  gathered  at  various  places,  from 
which  very  definite  conclusions  have  been  drawn  without  first  making 
allowance  for  the  variables  entering  into  the  problem  in  hand.  Unless 
a  high  degree  of  certainty  exists  that  the  results  secured  in  the  first 
trial  will  be  obtained  when  the  trial  is  repeated  the  experimental  data 
are  of  little  value. 


122  University  of  California  Publications  in  Agricultural  Sciences       [Vol.  4 

The  problem  of  variability  in  experimental  trials  with  field  crops 
has  formed  the  subject  of  a  number  of  recent  papers.1  It  is  not 
our  purpose  to  enter  into  a  discussion  of  the  problem  of  the  control 
of  field  experiments  from  the  crop  standpoint.  It  is  proposed,  how- 
ever, to  consider  the  possible  magnitudes  of  field  variation  in  soils 
and  the  bearing  of  such  variation  on  field  trials  in  which  the  soil 
mass  is  the  predominant  factor.  One  of  us  has  already  taken  up  this 
subject  from  the  standpoint  of  nitrate  production  in  soils,5  and  since 
no  data  are  obtainable  which  show  the  magnitude  of  the  variation 
in  some  of  the  constituents  commonly  measured  in  field  soils  it  is  of 
very  considerable  interest  to  present  data  which  have  been  obtained 
from  the  viewpoint  of  the  accurate  control  of  the  soil  as  a  variable 
factor.  It  must  be  understood  in  considering  the  data  presented  in  the 
following  pages  that  the  variations  found  and  the  statistical  constants 
computed  are  by  no  means  absolute  figures  which  can  be  taken  bodily 
and  applied  to  any  soil,  but  rather  that  they  will  serve  to  indicate  the 
extent  and  nature  of  the  variations  likely  to  be  found  in  field  soils, 
together  with  the  methods  which  it  is  hoped  will  prove  of  value  in 
allowing  for  such  variations  as  are  found  in  any  soil.  The  point 
has  previously  been  made  that  variations  in  the  soil  within  very 
limited  areas  may  be  so  great  as  to  render  results  secured  in  the  past, 
with  only  a  few  samples  taken  from  the  area,  of  very  limited  value. 
The  data  obtained,  since  the  first  paper  was  written,  and  presented 
in  this  and  the  following  papers  make  this  viewpoint  all  the  more 
secure. 

The  present  data  were  secured  in  connection  with  and  preliminary 
to  a  field  study  of  biologic  nitrogen  fixation  now  being  conducted  by 
this  laboratory,  and  though  incidental  to  that  problem  their  bearing 
upon  the  results  which  may  finally  be  secured  is  so  important  as  to 
render  their  consideration  from  that  viewpoint  of  much  interest.  This 
is  equally  true  of  field  experiments  of  a  similar  nature  which  have 
been,  or  are  being  conducted  elsewhere,  and  is  the  principal  reason 
for  the  presentation  of  the  following  data  at  the  present  time. 

Methods 

Two  fields  are  concerned  in  the  present  study,  one  on  the  University 
Farm  al  Davis  and  the  other  near  the  town  of  Oakley.  The  soils 
of  these  two  fields  are  of  very  different  character,  a  silty  clay  loam 
al   Davis,  and  a  blow  sand  at  Oaklev.     The  total  area  sampled  in  each 


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Pig.  1.     Diagram  of  areas  sampled,  showing  the  locations  from  which  the  samples  were  taken. 


Digitized  by  the  Internet  Archive 

in  2012  with  funding  from 

University  of  California,  Davis  Libraries 


http://archive.org/details/variabilityinsoi45wayn 


1919]      WaynicTc-Sliarp :  Variations  in  Nitrogen  and  Carbon  in  Field  Soils       123 

field  is  a  little  more  than  one  and  three-tenths  acres.  The  fields  were 
both  selected  for  their  apparent  uniformity,  both  being  nearly  level, 
with  no  changes  in  the  soil  mass  from  one  part  of  the  field  to  another 
great  enough  to  be  detected  by  the  usual  field  methods.  Both  fields 
were  practically  free  from  vegetation  when  selected,  and  before  the 
samplings  were  made  (March,  1918)  all  extraneous  material  had  been 
carefully  removed.  Since  the  data  presented  in  the  previous  paper 
were  the  only  data  which  would  serve  as  any  sort  of  a  guide  to  the 
number  of  samples  necessary  to  secure  the  degree  of  accuracy  desired, 
and  since  it  was  necessary,  further,  to  distribute  the  samples  in  such 
a  manner  as  to  cover  the  entire  area,  the  arrangement  shown  in 
figure  1  was  adopted.  It  will  be  noted  that  there  are  eighty  samples 
distributed  at  thirty-foot  intervals  over  the  entire  area,  forty  samples 
at  fifteen-foot  intervals  taken  from  five  different  parts  of  the  field, 
these  also  uniformly  distributed,  and  finally  twelve  samples  taken 
within  one  of  the  small  areas,  approximately  one-forty-eighth  of  an 
acre,  in  the  center  of  the  field.  There  are,  then,  one  hundred  samples 
from  each  area  under  consideration.  The  entire  number  of  samples 
will  be  treated  as  one  population,  except  in  so  far  as  they  are  useful 
in  showing  the  effect  of  the  distance  apart  samples  are  taken  upon 
the  variability,  and,  further,  the  relationship  of  the  variability  in 
a  given  small  area  within  a  field  to  that  of  the  entire  field.  It  is 
recognized  that  the  data  available  at  the  present  time  on  this  last  point 
are  limited,  due  to  the  small  number  of  samples  available,  but  they 
are  at  least  suggestive  of  the  relationship  between  the  two. 

All  the  samples  were  taken  uniformly  with  a  three-inch  soil  auger 
by  foot  sections.  As  soon  as  taken  each  foot  section  was  thoroughly 
mixed  and  approximately  one-half  of  the  sample  placed  in  a  quart 
jar  of  the  Mason  type.  When  all  the  samples  had  been  secured  the 
jars  were  placed  in  specially  constructed  boxes  and  shipped  by  express 
to  the  laboratory  at  Berkeley.  All  the  samples  were  there  reduced  to 
the  air-dry  condition  as  rapidly  as  possible  and  passed  through  a  two- 
millimeter  sieve.  The  determinations,  as  herein  reported,  were  made 
upon  the  mass  of  soil  passing  through  a  sieve  of  this  size. 

Total  nitrogen  was  determined  on  ten-gram  samples  of  the  Davis 
soil,  or  twenty-gram  samples  of  the  Oakley  soil,  using  the  modification 
of  the  Kjeldahl-Gunning  method  proposed  by  Hibbard.2  Eight  hun- 
dred cubic  centimeter  Pyrex  flasks  were  used  in  making  all  the 
determinations,  so  that  it  was  not  necessary  to  transfer  to  copper 
flasks  for  the  final  distillation.     All  the  titrations  were  made  with 


124  University  of  California  Publications  in  Agricultural  Sciences       [Vol.  4 

standard  hydrochloric  acid,  1  c.c.  of  which  was  equal  to  .54  milligrams 
of  nitrogen.  Determinations  for  total  carbon  were  made  upon  five 
and  ten  gram  samples,  respectively,  of  the  two  soils  by  a  modification 
of  the  wet  combustion  method  described  by  one  of  us  elsewhere.4 

Limits  of  Accuracy  of  Methods  for  Nitrogen  and  Carbon 

It  is  not  proposed  to  take  up  a  discussion  of  the  accuracy  of 
experimental  methods  in  general.  Before  experimental  work  with 
field  soils  is  undertaken  the  accuracy  of  the  laboratory  methods  to  be 
used  in  the  investigation  should  be  known.  This  is  true  because,  in 
the  first  instance,  any  factors  tending  toward  inaccurate  results  from 
the  laboratory  standpoint  are  possible  of  elimination  to  a  large  extent, 
and,  in  the  second  instance,  the  limitations  of  the  laboratory  method? 
may  finally  define  the  limits  of  accuracy  of  results  obtained  in  the 
field.  In  the  present  study,  all  errors  which  may  be  termed  accidental 
have  been  eliminated  so  far  as  possible  by  careful  attention  to  the 
details  of  manipulation. 

That  determinations  made  upon  the  different  portions  of  the  same 
sample  may  still  differ  considerably  among  themselves  is  shown  by 
an  inspection  of  tables  1  and  2,  where  a  number  of  determinations  for 
nitrogen  and  carbon  are  reported,  all  made  upon  the  same  soil  sample. 
The  results  presented  here  are  of  further  interest  in  showing  how 
nearly  values  found  for  a  composite  sample  may  conform  to  the  mean 
of  the  individual  samples  making  up  that  composite.  The  latter  point 
will  be  considered  more  at  length  later. 

Table  1. — Variability  of  Determinations  for  Total  Nitrogen  made  upon  a 

Uniform  Soil  Sample 


Nitrogen 

Deviation 

Nitrogen 

Deviation 

No. 

per  cent 

from  mean 

No. 

per  cent 

from  mean 

1 

.092 

.004 

16 

.096 

.000 

2 

.096 

.000 

17 

.093 

.003 

3 

.097 

.001 

18 

.097 

.001 

4 

.099 

.003 

19 

.096 

.000 

5 

.094 

.002 

20 

.097 

.001 

6 

.098 

.002 

21 

.101 

.005 

7 

.092 

.004 

22 

.098 

.002 

8 

.099 

.003 

23 

.097 

.001 

9 

.100 

.004 

24 

.099 

.003 

10 

.097 

.003 

25 

.096 

.000 

11 

.098 

.002 





12  • 

.097 

.001 

Mean  = 

.0960  ± 

.0030      .002 

13 

.092 

.004 

<r  = 

.0025  ± 

.0002 

14 

.090 

.000 

C. 

V.= 

2.60      ± 

0.24 

15 

.009 

.on:; 

1919]      Way  nick-Sharp :  Variations  in  Nitrogen  and  Carbon  in  Field  Soils       125 

Table   2. — Variability  of  Determinations   for  Total   Carbon   made  upon   a 

Uniform  Soil  Sample 


No. 

Carbon 
per  cent 

Deviation 
from  mean 

No. 

Carbon 
per  cent 

Deviation 
from  mean 

1 

1.093 

.012 

11 

1.081 

.000 

2 

1.076 

.005 

12 

1.093 

.012 

3 

1.077 

.004 

13 

1.076 

.005 

4 

1.092 

.011 

14 

1.073 

.008 

5 

1.065 

.016 

15 

1.082 

.001 

6 

1.092 

.011 

16 

1.069 

.012 

7 

1.091 
1.091 

.010 
.010 

8 

Mean 

=  1.081  ± 

.0015 

.008 

9 

1.080 

.001 

cr 

=    .009  ± 

.001 

10 

1.071 

.010 

C. 

V. 

=    .83    ± 

.09 

If  a  number  of  determinations  are  made  upon  a  given  sample  and 
the  values  so  secured  are  arranged  according  to  the  frequency  of  their 
occurrence  it  will  be  found  that  they  group  themselves  after  the  man- 
ner of  a  normal  error  curve.  This  fact  has  already  been  discussed 
in  connection  with  the  determination  of  nitrates  by  the  colorimetric 
method  and  is  introduced  here  because  it  serves  as  a  background  for 
the  consideration  of  limits  of  accuracy  of  the  methods  under  dis- 
cussion. Since  a  series  of  results  such  as  given  in  table  1  or  2  do 
follow  a  normal  error  curve,  we  are  justified  in  using  the  statistical 
constants  calculated  from  them  as  a  measure  of  the  accuracy  of  our 
methods.  We  have,  for  example,  in  the  case  of  nitrogen,  the  mean 
of  twenty-five  determinations,  expressed  as  .0960  ±  .0003%.  This 
mean  is,  then,  probably  correct  to  within  ±0.31%  of  the  actual 
amount  of  nitrogen  determined.  If,  however,  but  a  single  determina- 
tion had  been  made  it  would  have  been  subject  to  a  probable  error 
of  .0960  ±  .0016%  of  ±1.66%  of  the  amount  of  nitrogen  found. 
On  the  other  hand,  the  probable  error  of  the  mean  of  one  hundred 
total  nitrogen  determinations  amounts  to  ±  .00016 %,  or  ±  .016%  of 
the  nitrogen  present.  It  is  evident,  therefore,  that  the  larger  the 
number  of  determinations  made  upon  any  given  sample  the  greater 
will  be  the  accuracy  of  the  mean  of  the  determinations  made,  but  only 
in  proportion  to  the  square  root  of  their  number.  It  is  possible  on  this 
basis  to  determine  the  amount  of  nitrogen  present  in  any  soil  with 
a  very  high  degree  of  accuracy,  provided  a  sufficient  number  of  deter- 
minations can  be  made.  This  conception  is  derived  from  the  fact  that 
what  we  have  chosen  to  term  the  laboratory  error  is  purely  a  matter 
of  chance.  Therefore,  a  series  of  these  errors,  whether  derived  from 
several  determinations  on  a  single  sample  or  from  individual  deter- 
minations on  different  samples,  if  plotted  by  classes,  would  be  dis- 


126  University  of  California  Publications  in  Agricultural  Sciences       [Vol.  4 

tributed  as  a  normal  frequency  curve  in  accordance  with  the  laws 
of  chance.  Computations  of  such  a  series  of  errors  would  yield  the 
same  statistical  constants  whether  the  errors  were  from  the  deter- 
minations made  on  a  single  sample  or  were  secured  from  single 
determinations  made  on  separate  samples.  This  point  is  of  impor- 
tance, and  unless  recognized  before  any  determinations  are  made  upon 
soil  taken  from  any  experimental  area,  many  determinations  may 
be  made  which  will,  in  the  final  analysis,  lend  nothing  to  the  final 
accuracy  of  the  results.  This  is  true  when  we  are  dealing  with  the 
mean  of  a  representative  number  of  determinations.  The  worker  may 
carry  through  his  determination  in  duplicate  or  in  triplicate,  but  such 
a  practice  will  only  serve  to  satisfy  him  as  to  the  accuracy  of  his  own 
manipulation,  as  such  replications  are  of  no  value  when  a  statistical 
interpretation  of  the  data  as  a  whole  is  made. 

That  the  laboratory  error  is  small  when  compared  with  the 
variation  found  in  field  samples  is  shown  by  the  following  data,  which 
have  been  computed  on  a  "pounds  per  acre"  basis,  using  4,000,000 
pounds  as  the  weight  of  one  acre  foot  of  soil.  If  twenty-five  samples 
are  taken  the  error  which  may  be  attributed  to  laboratory  manipula- 
tion amounts  to  plus  or  minus  twelve  pounds  per  acre,  with  an  even 
chance  that  our  results  are  accurate  to  this  amount.  If  we  adopt  a 
thirty-to-one  chance  as  the  largest  chance  which  we  deem  it  safe  to 
take  in  order  that  our  results  will  have  a  high  degree  of  accuracy,  the 
lowest  significant  figure  amounts  to  plus  or  minus  thirty-eight  pounds 
per  acre.  In  other  words,  with  twenty-five  determinations  increases 
or  decreases  in  the  nitrogen  found  must  exceed  this  figure  before  they 
reach  a  magnitude  sufficiently  great  to  be  attributable  to  any  treat- 
ment which  we  have  applied.  On  the  same  basis,  the  mean  of  our 
total  number  of  one  hundred  samples  is  probably  accurate  to  within 
twenty  pounds  per  acre  so  far  as  the  laboratory  error  itself  is  con- 
cerned. However,  when  we  consider  that  the  error  due  to  the  varia- 
tions in  field  samples  amounts  to  two  hundred  and  forty  pounds  per 
acre  on  an  even  chance,  or  seven  hundred  and  sixty  pounds  on  a 
thirty-to-one  chance,  it  is  seen  that  the  laboratory  error  of  twenty 
pounds  becomes  relatively  insignificant.  When  we  are  dealing  with 
the  number  of  samples  used  in  the  present  study,  together  with  the 
relatively  large  amount  of  nitrogen  determined,  in  the  case  of  the 
Davis  soil  at  least,  it  is  evident  that  this  laboratory  error  may  be 
safely  disregarded.  It  is  recognized,  however,  that  there  may  be 
instances  in  which  the  laboratory  error  may  limit  to  a  large  degree 


1919]      W  ay  niclc- Sharp :  Variations  in  Nitrogen  and  Carbon  in  Field  Soils       127 

the  accuracy  to  be  expected  from  the  use  of  a  given  number  of  field 
samples.  This  might  be  true,  for  example,  in  a  case  in  which  the 
total  amount  of  nitrogen  or  any  other  element  determined  is  so  small 
that  the  laboratory  error  becomes  relatively  of  large  magnitude.  It 
must  always  be  borne  in  mind,  however,  that  the  curve  representing 
the  laboratory  errors  and  the  one  representing  the  errors  due  to 
sampling  are  always  parallel;  that  is,  the-  two  variables  always 
decrease  in  the  same  ratio  as  the  number  of  samples  is  increased. 

The  above  discussion  has  been  limited  to  a  consideration  of  the 
probable  accuracy  of  the  nitrogen  determination,  and  it  has  been 
treated  somewhat  at  length  because  it  is  considered  important  that 
there  should  be  a  clear  understanding  of  the  limitations  of  the 
methods  employed.  The  same  mode  of  treatment  might  be  followed 
in  discussing  the  limits  of  accuracy  of  the  carbon  determination. 
These  results  will  not  be  taken  up  in  detail.  Suffice  it  to  say  that 
the  laboratory  error  attributable  to  our  method  may  be  taken  as 
amounting  to  seventy-two  pounds  per  acre  on  a  thirty-to-one  chance, 
while  the  mean  of  one  hundred  samples  has  a  probable  error,  on  the 
same  basis,  due  to  field  variability,  of  approximately  eight  hundred 
pounds  per  acre. 

We  have  deemed  it  important  to  take  up  a  discussion  of  the  limits 
of  accuracy  of  the  methods  used  in  order  that  a  false  estimation  of 
the  accuracy  of  the  measurements  made  may  not  be  assumed.  Many 
determinations  have  been  reported  in  the  past  giving  increases  or 
decreases  in  the  constituents  commonly  measured  in  field  soils  without 
consideration  of  the  accuracy  of  the  methods  employed.  For  example, 
the  amount  of  nitrogen  removed  by  an  average  crop  of  barley  is 
usually  stated  as  about  forty  pounds  per  acre.  We  have  shown  that 
by  making  twenty-five  determinations  on  a  single  soil  sample,  we  are 
able,  due  to  our  laboratory  errors,  to  determine  nitrogen  in  amount 
not  less  than  plus  or  minus  thirty-eight  pounds  per  acre,  which  is 
practically  the  same  figure  as  given  for  the  nitrogen  removed  by  a 
single  crop.  It  is  evident,  therefore,  that  we  are  just  able  to  deter- 
mine the  amount  of  nitrogen  removed  by  a  single  crop  from  deter- 
minations made  upon  the  soil  when  the  soil  mass  has  been  made  as 
uniform  as  it  could  be  made  experimentally  and  a  large  number  of 
determinations  carried  out  on  a  soil  so  prepared.  In  other  words,  if 
we  ignore  the  variability  of  the  field  samples  and  consider  only  our 
laboratory  error  it  is  found  that  the  value  for  the  nitrogen  removed 
by  a  single  crop  and  that  for  the  error  due  to  laboratory  manipulations 


128  University  of  California  Publications  in  Agricultural  Sciences       [Vol.  4 

is  of  nearly  the  same  magnitude.  When  we  take  into  account  as  well 
the  errors  due  to  sampling  in  the  field,  it  is  evident  that  the  differences 
which  must  be  secured  before  we  can  feel  confident  that  the  results 
are  reliable  are  very  much  larger. 

When  the  results  of  past  soil  investigations  are  examined  from 
this  viewpoint  it  will  be  found  that  most  of  them  have  been  obtained 
under  conditions  so  imperfectly  controlled  or  under  variations  in 
sampling  so  inadequately  taken  into  account,  as  to  render  the  results 
obtained  of  very  questionable  value. 


Experimental  Data 

The  experimental  data  for  the  two  areas  are  reported  in  tables  3 
and  4.  It  will  be  noted  that  the  extreme  range  for  nitrogen  in  the 
Davis  soil  is  from  .077  to  .124%  and  in  the  Oakley  soil  from  .022  to 
.063%,  a  difference  between  the  extremes  of  about  60%  in  the  first 
soil  and  nearly  300%  in  the  second.  If  we  translate  these  figures  into 
a  "pounds  per  acre"  basis,  we  have  a  range  of  from  3100  to  5000 
pounds  in  the  first  soil  and  from  900  to  2500  in  the  second  soil.  For 
carbon  the  range  is  from  0.903  to  1.383%  in  the  Davis  soil  and  from 
0.252  to  0.750%  in  the  Oakley  soil,  a  percentage  difference  between 
the  extremes  of  nearly  the  same  magnitude  as  that  given  for  nitrogen. 
Expressed  on  the  acre  basis  in  the  same  manner  as  the  nitrogen  figures 
given  above,  we  have  36,000  to  55,000  pounds  and  10,000  to  30,000 
pounds  respectively  for  the  two  soils.  If  but  a  single  sample  were 
taken  at  random  to  represent  these  two  areas,  it  can  be  readly  seen 
that  a  very  inaccurate  estimation  of  their  nitrogen  and  carbon  content 
might  be  made.  Further,  it  is  probable  that  these  differences  between 
samples  taken  from  apparently  uniform  areas  are  quite  as  large 
as  any  that  may  be  found  between  different  soil  types.  In  fact,  the 
figures  here  presented  are  extremely  interesting  from  that  viewpoint, 
in  that,  while  it  may  be  contended  that  different  soil  types,  as  usually 
determined,  have  a  range  of  values  for  total  nitrogen,  for  instance, 
not  covered  by  another  soil  type,  unless  a  large  number  of  samples  are 
taken,  it  would  be  out  of  the  question  to  distinguish  between  two  soil 
types  on  that  basis.  For  example,  in  the  two  soils  under  consideration, 
which  are  nearly  as  widely  separated  as  soil  types  can  be,  one  a  silty 
clay  loam  and  the  other  a  blow  sand,  the  difference  between  the  high 
valne  for  nitrogen  in  one  and  the  low  value  for  nitrogen  in  the  other 
amounts  to  only  .014%,  or  less  than  a  third  of  the  extreme  range  in 


1919]      W  ay  nick- Sharp :  Variations  in  Nitrogen  and  Carbon  in  Field  Soils       129 

either  of  these  soils.  This  is  a  very  small  value  when  we  take  into 
consideration  the  variability  of  the  soil  as  a  whole.  In  this  connec- 
tion, it  is  again  emphasized  that  we  are  dealing  with  two  very  limited 
areas,  selected  because  of  their  apparent  uniformity. 

It  will  be  noted  that  the  coefficients  of  variability  for  both  nitrogen 
and  carbon  are  9.00%  in  the  Davis  soil,  while  in  the  Oakley  soil  they 
are  much  in  excess  of  this  figure,  being  21.87%  for  nitrogen  and 
21.11%  for  carbon.  It  will  be  recognized  that  the  coefficients  of 
variability  for  the  Davis  soil  as  regards  the  two  constituents  here 
measured  are  low,  so  that  this  area  may  be  properly  considered  as 
possessing  a  relatively  high  degree  of  uniformity.  Just  how  true  this 
is  as  regards  other  constituents  will  be  brought  out  in  a  subsequent 
paper.  The  figures  as  here  given  may  be  used  again  to  emphasize 
the  statement  made  in  the  introduction  of  this  paper  to  the  effect 
that  values  found  for  one  soil  may  be  very  misleading  if  an  attempt 
is  made  to  apply  them  as  an  aid  in  forming  a  judgment  of  the  probabk 
variation  to  be  found  in  another  soil. 


Effect  of  Distance  on  Variability  of  Samples 

It  has  already  been  stated  that  because  of  the  locations  used  in 
sampling  it  is  possible  to  arrange  our  data  in  such  a  manner  that  we 
may  calculate  the  statistical  constants  for  any  number  of  samples 
taken  at  intervals  of  thirty,  fifteen  or  ten  feet.     The  samples  taken 

Table  3. — Total  Nitrogen  and  Carbon  in  Various  Samples  of  the  Davis  Soil 


No.  of 
sample 
1 

Nitrogen 

per  cent 

.104 

Carbon 

per  cent 

1.167 

No.  of 
sample 

18 

Nitrogen 

per  cent 

.099 

Carbon 

per  cent 

1.048 

2 

.086 

1.048 

19 

.086 

0.965 

3 

.080 

0.958 

20 

.093 

1.040 

4 

.092 

1.069 

21 

.092 

1.014 

5 

.099 

1.071 

22 

.105 

1.122 

6 

.098 

1.132 

23 

.123 

1.329 

7 

.107 

1.124 

24 

.107 

1.075 

8 

.117 

1.195 

25 

.096 

1.048 

9 

.105 

1.059 

26 

.088 

0.978 

10 

.093 

1.084 

27 

.100 

1.091 

11 

.086 

1.077 

28 

.106 

0.998 

12 

.091 

0.997 

29 

.105 

1.147 

13 

.082 

0.896 

30 

.104 

1.112 

14 

.105 

1.198 

31 

•  .110 

1.154 

15 

.114 

1.218 

32 

.115 

1.244 

16 

.108 

1.157 

33 

.093 

0.997 

17 

.094 

0.970 

34 

.103 

1.052 

130  University  of  California  Publications  in  Agricultural  Sciences       [Vol.  4 


Table  3. 


No.  of 
sample 

Nitrogen 
per  cent 

35 

.101 

36 

.106 

37 

.103 

38 

.113 

39 

.110 

40 

.111 

41 

.093 

42 

.091 

43 

.096 

44 

.100 

45 

.097 

46 

.096 

47 

.104 

48 

.116 

49 

.093 

50 

.109 

51 

.107 

52 

.102 

53 

.106 

54 

.106 

55 

.118 

56 

.124 

57 

.101 

58 

.090 

59 

.101 

60 

.101 

61 

.098 

62 

.098 

63 

.107 

64 

.101 

65 

.086 

66 

.103 

67 

.088 

68 

.094 

69 

.100 

70 

.097 

Carbon 
per  cent 

1.045 

1.019 

1.120 

1.215 

1.202 

1.167 

1.007 

0.973 

1.100 

1.135 

1.052 

1.034 

1.090 

1.252 

0.993 

1.180 

1.126 

1.153 

1.256 

1.250 

1.254 

1.383 

0.973 

1.001 

0.973 

1.120 

1.051 

1.101 

1.195 

1.254 

1.088 

1.137 

1.009 

1.078 

1.173 

1.071 


{Continued) 

No.  of 
sample 

Nitrogen 
per  cent 

71 

.106 

72 

.116 

73 

.077 

74 

.090 

75 

.095 

76 

.093 

77 

.101 

78 

.104 

79 

.106 

80 

.116 

81 

.103 

82 

.091 

83 

.078 

84 

.091 

85 

.094 

86 

.096 

87 

.099 

88 

.107 

89 

.115 

90 

.103 

91 

.112 

92 

.116 

93 

.102 

94 

.098 

95 

.095 

96 

.097 

97 

.098 

98 

.099 

99 

.097 

100 

.103 

Carbon 
per  cent 

1.168 

1.365 

0.977 

1.161 

1.048 

1.123 

1.267 

1.107 

1.186 

1.289 

1.108 

0.986 

0.903 

1.161 

1.000 

1.042 

1.288 

1.352 

1.232 

1.109 

1.251 

1.322 

1.088 

0.989 

1.997 

1.093 

1.114 

1.063 

1.064 

1.092 


Mean  =  .100  ±  .006  1.110  ±  .007 

A.  D.  =  .006  .083 

a~  .0090  ±  .0006  .1000  ±  .0005 

C.  V.  =  9.00  ±  0.42  9.00  ±  0.42 


Tarle  4. — Total  Nitrogen  and  Carbon  in  Various  Samples  of  the  Oakley  Soil 


No.  of 
sample 

Nitrogen 
per  cent 

Carbon 
per  cent 

No.  of 
sample 

Nitrogen 
per  cent 

Carbon 
per  cent 

1 

.042 

.624 

10 

.032 

.420 

2 

.032 

.417 

11 

.024 

.330 

3 

.027 

.365 

12 

.024 

.361 

4 

.022 

.179 

13 

.031 

.349 

5 

.029 

.355 

14 

.032 

.314 

6 

.026 

.383 

15 

.033 

.475 

7 

.027 

.279 

16 

.042 

.330 

8 

.031 

.404 

17 

.042 

.499 

9 

.042 

.565 

18 

.028 

.314 

1919]      W  ay  nick-Sharp :  Variations  in  Nitrogen  and  Carbon  in  Field  Soils       131 


Table  4.- 

— (Continued) 

No.  of 
sample 

Nitrogen 
per  cent 

Carbon 
per  cent 

No.  of 
sample 

Nitrogen 
per  cent 

Carbon 
per  cent 

19 

.027 

.402 

63 

.032 

.466 

20 

.021 

.428 

64 

.034 

.450 

21 

.037 

.421 

65 

.045 

.647 

22 

.022 

.308 

66 

.028 

.384 

23 

.036 

.345 

67 

.030 

.480 

24 

.034 

.345 

68 

.031 

.362 

25 

.041 

.524 

69 

.035 

.498 

26 

.029 

.377 

70 

.033 

.407 

27 

.025 

.382 

71 

.039 

.577 

28 

.029 

.450 

72 

.031 

.431 

29 

.034 

.453 

73 

.061 

.947 

30 

.026 

.292 

74 

.040 

.589 

31 

.027 

.345 

75 

.041 

.612 

32 

.031 

.450 

76 

.040 

.636 

33 

.042 

.507 

77 

.063 

.750 

34 

.027 

.314 

78 

.036 

.478 

35 

.026 

.341 

79 

.040 

.587 

36 

.028 

.252 

80 

.035 

.516 

37 

.035 

.319 

81 

.029 

.368 

38 

.027 

.346 

82 

.025 

.361 

39 

.026 

.368 

83 

.022 

.329 

40 

.031 

.524 

84 

.035 

.409 

41 

.052 

.450 

85 

.032 

.558 

42 

.030 

.314 

86 

.030 

.384 

43 

.031 

.396 

87 

.036 

.380 

44 

.028 

.381 

88 

.032 

.497 

45 

.032 

.502 

89 

.033 

.436 

46 

.029 

.404 

90 

.024 

.312 

47 

.030 

.480 

91 

.033 

.396 

48 

.032 

.382 

92 

.028 

.366 

49 

.046 

.426 

93 

.027 

.407 

50 

.031 

.718 

94 

.026 

.338 

51 

.033 

.456 

95 

.029 

.314 

52 

.032 

.488 

96 

.027 

.360 

53 

.034 

.443 

97 

.029 

.396 

54 

.033 

.450 

98 

.037 

.435 

55 

.034 

.516 

99 

.029 

.382 

56 

.033 

.352 

100 

.029 

.347 

57 

.052 

.742 





58 

.034 

.461 

Mean  = 

=  .032  ±  .005 

.440  ±  .007 

59 

.031 

.475 

A.D.= 

=  .007 

.009 

60 

.031 

.534 

a  - 

=  .0070  ±  .0003 

.115  ±  .005 

61 

.031 

.420 

C.V.= 

=  21.87  ±  1.03 

25.11  ±  1.13 

62 

.032 

.458 

at  the  last  two  distances  were  not  uniformly  distributed  over  the 
entire  area  but  represent  smaller  areas  within  the  larger.  They  are 
none  the  less  useful  in  forming  an  estimate  of  the  relation  which  a 


132  University  of  California  Publications  in  Agricultural  Sciences       [Vol.4 

small  area  may  bear  to  a  larger  area  within  which  it  is  located,  or, 
as  an  interrogation,  would  we  be  justified  in  applying  the  value 
obtained  for  nitrogen  in  a  plot  of  %o  °f  an  acre  to  tliat  iR  one  acre  • 
In  the  case  of  the  Davis  soil  we  may  answer  this  question  in  the 
affirmative,  since  there  is  no  significant  difference  between  the  mean 
of  amounts  of  nitrogen  found  in  the  total  population  as  related  to 
the  samples  taken  at  either  the  fifteen  or  ten  foot  intervals  as  shown 
in  table  5.  With  the  carbon  determinations  the  differences  are  slight. 
It  will  be  noted,  however,  that  the  coefficients  of  variability  of  the 
samples  taken  at  ten  foot  intervals  is  only  about  one-third  as  large 
as  those  found  for  the  total  population.  With  the  Oakley  soil,  on  the 
other  hand,  there  is  a  significant  difference  in  the  means  for  both  total 
nitrogen  and  total  carbon  for  the  samples  taken  at  fifteen  and  at  ten 
foot  intervals.  In  other  words,  in  dealing  with  a  soil  as  variable  as 
regards  nitrogen  and  carbon  as  the  Oakley  soil  we  would  not  be  justi- 
fied in  using  the  data  obtained  from  a  small  area  in  the  interpretation 
of  that  secured  from  the  larger.  The  coefficient  of  variability  of  the 
samples  taken  at  shorter  intervals  is  significantly  less  than  that  cal- 
culated from  the  total  population,  although  the  difference  between  the 
two  is  less  than  half  the  coefficient  of  variability  calculated  for  the 
total  population  in  either  case. 

These  data  emphasize  again  the  point  which  was  brought  out  in 
the  previous  paper,  that  it  is  very  unwise  to  judge  an  area  even  of 
the  size  reported  here  by  values  obtained  from  a  limited  portion  of 
that  area  if  the  variations  are  of  the  magnitude  reported  for  the 
Oakley  soil.  Estimations  so  made  may  be  far  from  the  truth  and  if 
extended  in  their  application  may  lead  to  very  erroneous  conclusions. 
Accuracy  of  Values  Secured  by  Using  Composite  Soil  Samples 

From  the  standpoint  of  the  amount  of  labor  involved  in  making 
determinations  in  the  laboratory  the  compositing  of  a  number  of 
individual  samples  is  very  desirable.  Such  a  practice  is  permissible, 
however,  only  when  the  variations  amongst  individual  samples  in  the 
area  under  consideration  are  known.  When  a  larger  area  is  broken  up 
into  plots  the  compositing  of  a  number  of  samples  taken  in  a  repre- 
sentative manner  from  a  small  plot  becomes  almost  necessary,  since 
otherwise  the  amount  of  work  involved  in  making  the  determinations 
on  a  large  number  of  individual  samples  would  be  almost  prohibitive. 
To  test  this  point,  the  determinations  reported  in  tables  1  and  2  were 
made  on  a  composite  sample,  prepared  by  taking  twenty  grams  from 
each  of  the  samples  of  the  Davis  soil,  numbered  from  2  to  26  inclusive. 


1919]      W  ay  nick- Sharp :  Variations  in  Nitrogen  and  Carbon  in  Field  Soils       133 


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134  University  of  California  Publications  in  Agricultural  Sciences       [Vol.  4 

Just  how  closely  the  results  agree  is  shown  in  table  6.  In  the  case  of 
both  nitrogen  and  carbon  the  probable  error  in  the  difference  between 
the  two  results  is  approximately  equal  to  the  difference  between  the 
two  results,  hence  the  latter  value  is  of  no  significance. 

It  must  be  remembered,  however,  that  we  have  made  a  large 
number  of  determinations  on  the  composite  sample,  so  that  we  have 
secured  a  much  higher  degree  of  accuracy  than  if  but  one  or  two 
determinations  had  been  made.  The  making  of  a  composite  sample 
is,  therefore,  a  justifiable  procedure  from  the  standpoint  of  the  final 
accuracy  of  the  results  secured;  provided,  of  course,  that  enough 
determinations  are  made  upon  the  sample  so  that  their  mean  will 
accurately  represent  the  soil  mass,  and,  further,  that  the  composite 
itself  represents  equal  amounts  of  the  various  individual  samples 
which  have  themselves  been  made  as  uniform  as  possible  by  thorough 
mixing. 

Table  6. — Showing  the  Eelation  Between  Determinations  Made  Upon 

Individual  Samples  and  on  a  Composite  Sample  made  from  the 

Various  Individual  Samples 

Mean  Probable  error  of  mean 

* ,  , * , 

Nitrogen  Carbon  Nitrogen  Carbon 
Determinations  from  compo- 
site  sample  Nos.   2-26   in- 
clusive     0960                 1.081                   .0003  .0015 

Determinations  on  individ- 
ual samples  Nos.  2-26  in- 
clusive     0940  1.075  .0015  .0058 

Difference    0020  .006  .0015  .0059 


Number  of  Field  Samples  Necessary  to  Secure  the  Degree 
of  Accuracy  Desired 

We  may  adopt  as  the  limit  of  accuracy  to  be  secured  in  any  investi- 
gation a  value  below  which  we  attach  no  significance  to  our  results. 
The  limiting  values  which  may  be  taken  will  depend  largely  upon  the 
anticipated  significance  to  be  given  to  the  results  secured  from  the 
experiment  in  hand.  Further,  the  physical  capacity  of  the  laboratory 
carrying  on  the  experimental  work  will  in  many  instances  be  the 
factor  limiting  the  number  of  samples  and  thus  the  probable  accuracy 
secured.  When  it  is  realized  that  the  results  obtained  even  by  the 
most  careful  laboratory  procedure,  carried  out  with  a  larger  number 


1919]      Waynich-Sharp :  Variations  in  Nitrogen  and  Carbon  in  Field  Soils       135 

of  samples  than  heretofore  used,  may  still  be  in  error  to  such  a  degree 
that  only  large  increases  or  decreases  in  soil  constituents  may  be 
measured  with  accuracy,  the  importance  of  using  as  many  samples  as 
the  capacity  of  the  laboratory  will  permit  becomes  evident. 

To  emphasize  the  importance  of  a  correct  estimate  of  the  number 
of  samples  necessary  to  measure  certain  changes  in  carbon  and  nitro- 
gen which  may  take  place  in  the  two  soils  under  discussion,  the  values 
given  in  table  7  have  been  calculated  after  the  manner  outlined  in 
a  previous  publication.5  In  the  second  column  the  differences  which 
we  desire  to  measure  are  expressed  on  a  "pounds  per  acre"  basis, 
while  in  the  third  column  these  differences  are  given  on  a  basis  of 
percentage  of  soil,  allowing  4,000,000  pounds  per  acre  foot.     In  the 

Table  7. — Estimate  of  the  Number  of  Samples  Eequired  for  Accurate 
Measurement  of  Certain  Changes  in  Nitrogen  and  Carbon 


Limits  of 

Limits  of 

Davis  Soil 

accuracy 
pounds 
per  acre 

accuracy 

percentage 

basis 

Odds  1-1 

Odds  10-1 

Odds  30- 

Nitrogen 

25 

.0006 

100 

250 

317 

50 

.0012 

25 

62 

79 

100 

.0024 

6 

15 

19 

250 

.0062 

.9 

2 

3 

500 

.0125 

.2 

1 

1 

Carbon 

25 

.0006 

12222 

30555 

38743 

50 

.0012 

3055 

7637 

9684 

100 

.0024 

764 

1910 

2425 

250 

.0062 

114 

285 

361 

500 

.0125 

28 

70 

88 

Oakley  Soil 

Nitrogen 

25 

.0060 

61 

125 

193 

50 

.0012 

15 

37 

47 

100 

.0024 

4 

10 

12 

250 

.0062 

.6 

1 

2 

500 

.0125 

.1 

1 

1 

Carbon 

25 

.0006 

16685 

41712 

52891 

50 

.0012 

4170 

10452 

13218 

100 

.0024 

1042 

2605 

3303 

250 

.0062 

156 

390 

494 

500 

.0125 

39 

97 

123 

next  three  columns  is  stated  the  number  of  samples  necessary  to  take 
so  that  their  mean  will  have  a  probable  error  no  greater  than  that 
given  in  columns  two  and  three.  The  number  of  samples  required 
is  listed  under  three  headings,  depending  upon  the  chances  we  are 
willing  to  take  that  our  experimental  results  can  be  duplicated  under 


136  University  of  California  Publications  in  Agricultural  Sciences       [Vol.  4 

the  same  conditions.  With  odds  of  one  to  one,  the  chances  are  even 
that  our  experimental  results  are  capable  of  duplication.  With  odds 
of  ten  to  one  or  thirty  to  one  the  chances  are  that  in  one  hundred  trials 
ten  and  three  of  them,  respectively,  will  not  give  the  same  results  as 
our  original  experiment. 

It  will  be  noted  that  if  we  accept  twenty-five  pounds  per  acre  as 
our  limiting  value  for  nitrogen  we  must  take  no  less  than  317  samples 
from  the  Davis  soil  or  193  samples  from  the  Oakley  soil  with  odds  of 
thirty  to  one.  With  carbon  to  be  determined,  no  fewer  than  38,743 
and  52,891  samples,  respectively,  of  the  two  soils  must  be  taken.  It 
is  at  once  evident  that  these  samples  are  too  numerous  from  the 
standpoint  of  maintaining  the  integrity  of  the  plot  we  are  sampling 
or  the  capacity  of  the  laboratory  to  handle  the  samples.  We  must, 
therefore,  content  ourselves  with  a  lower  degree  of  accuracy  than 
twenty-five  pounds  per  acre.  As  we  increase  our  limiting  value 
the  necessary  number  of  samples  decreases  very  rapidly,  so  that 
with  a  value  of  about  one  hundred  pounds  of  nitrogen  per  acre  we 
require  but  nineteen  samples  of  the  Davis,  or  twelve  samples  of  the 
Oakley  soil.  For  the  investigation  in  hand  we  have  taken  eighty 
pounds  of  nitrogen  and  eight  hundred  pounds  of  carbon  per  acre  as 
our  limiting  values,  which  makes  it  necessary  to  use  twenty-eight 
samples  for  nitrogen  in  the  Davis  soil  and  nineteen  in  the  Oakley 
soil,  with  forty-eight  and  forty-one  samples,  respectively,  for  carbon. 
These  values  were  chosen  because  this  number  of  samples  is  within 
the  capacity  of  the  laboratory  to  make  the  determinations  when  we 
take  into  consideration  the  number  of  different  plots  under  treatment. 
It  is  true,  then,  that  when  the  investigation  is  finished,  we  will  know 
that  our  results  will  not,  with  odds  of  thirty  to  one,  have  a  probable 
accuracy  greater  than  the  figures  given  above.  With  the  chances  but 
even  that  we  may  be  able  to  repeat  our  experiment  and  obtain  the 
same  results  as  secured  when  the  trial  was  originally  carried  out  the 
work  involved  in  carrying  through  the  original  experiment  is  scarcely 
justified.  Even  odds  of  ten  to  one  leave  a  large  chance  for  error  when 
attempts  are  made  to  repeat  the  experiment.  We  are  hardly  justified 
in  taking  a  larger  chance  than  thirty  to  one,  for  our  experimental 
results  will  still  probably  fail  of  replication  three  times  out  of  every 
hundred  trials.  Some  field  experiments  may  not  justify  the  work 
involved  in  sampling  to  secure  the  degree  of  certainty  desired  in  the 
present  experiment.  This  may  be  so  if  the  results  so  secured  are  to 
have  a  very  limited  application  or  are  of  a  preliminary  nature.     In 


1919]      Waynick-Sharp :  Variations  in  Nitrogen  and  Carbon  in  Field  Soils       137 

general,  however,  it  is  felt  that  a  larger  chance  than  the  one  taken 
in  this  experiment  is  hardly  justified  and  may  only  lead  to  further 
confusion  in  our  interpretation  of  data  secured  through  field  experi- 
mentation. 

It  will  be  noted  that  fractional  values  are  given  in  four  instances. 
They  are  given  only  as  the  results  of  calculation  as  the  taking  of  a 
fraction  of  a  sample  is  obviously  impossible.  It  must  be  remembered, 
however,  that  in  using  a  small  number  of  samples  the  laboratory  error 
may  be  great  enough  to  invalidate  the  results  secured  unless  a  sufficient 
number  of  determinations  is  made  to  reduce  this  error  to  a  low  value. 

By  the  use  of  the  method  suggested  for  the  calculation  of  the 
number  of  samples  necessary  to  secure  any  desired  degree  of  accuracy, 
two  ends  are  attained.  In  the  first  place,  the  sampling  of  field  soils 
becomes  not  something  to  be  done  in  a  haphazard  sort  of  way,  but 
rather  a  definite,  practical  procedure,  the  results  of  which  may  be 
predicted  with  a  high  degree  of  certainty.  In  the  second  place, 
much  needless  work  may  be  avoided  where  more  samples  are  taken 
than  are  really  necessary  to  ensure  the  degree  of  accuracy  desired. 

As  we  have  already  stated  before,  we  do  not  think  our  data 
sufficiently  extensive  to  warrant  a  definite  statement  on  the  relation 
between  the  total  area  reserved  for  experimental  purposes  and  small 
subdivisions  made  from  that  area.  In  general,  it  is  probably  true 
that  small  areas  are  less  variable  than  the  larger  areas  within  which 
the  former  are  located.  That  this  may  not  always  hold  true  is  shown 
by  the  data  for  the  nitrate  found  in  the  field  soil  reported  in  a  previous 
paper,  and,  to  a  large  extent,  holds  true  for  the  data  presented  in 
this  paper  for  the  Oakley  soil.  It  is  hoped  that  as  our  work  progresses 
with  these  two  experimental  plots  we  may  secure  data  which  will 
be  of  value  in  interpreting  the  relation  of  small  areas  to  larger,  and 
from  such  data  we  may  likewise  be  able  to  correct,  to  a  certain  extent, 
for  the  heterogeneity  in  field  soils  after  the  contingency  method  pro- 
posed by  Surface  and  Pearl.3 


138  University  of  California  Publications  in  Agricultural  Sciences       [Vol.  4 


SUMMARY 

Data  are  presented  in  the  present  paper  showing  the  variations 
found  in  total  nitrogen  and  total  carbon  in  two  experimental  areas, 
located  upon  soils  of  widely  different  types.  Statistical  methods  are 
applied  to  the  interpretation  of  the  results  obtained.  The  following 
statements  seem  justified  from  the  results  secured: 

1.  The  extreme  variations  between  different  samples  in  which 
nitrogen  and  carbon  were  determined  are  of  very  considerable  mag- 
nitudes and  show  that  the  results  secured  with  one  or  a  few  samples 
would  be  likely  to  be  unreliable. 

2.  It  is  unwise  to  attempt  to  apply  the  statistical  constants  cal- 
culated for  one  area  to  other  areas  even  though  in  themselves  appar- 
ently uniform  since  the  respective  variabilities  may  be  very  different. 

3.  Data  are  presented  showing  the  making  of  a  composite  sample 
to  be  fully  justified  after  the  variations  in  the  area  to  be  sampled  are 
known. 

4.  The  relation  of  variations  in  a  small  area  to  differences  between 
soil  types,  based  upon  the  constituents  determined  is  discussed,  and 
the  conclusion  is  drawn  that  only  after  very  careful  sampling  may 
such  differences  be  determined  with  certainty. 

5.  The  advantages  of  estimating  the  number  of  samples  necessary 
to  secure  any  degree  of  accuracy  are  discussed.  It  is  shown  that  a 
higher  degree  of  certainty  in  experimental  work  may  be  secured  by  so 
doing,  and  also  that  in  some  instances  needless  labor  may  be  elim- 
inated. 

In  the  past  many  erroneous  conclusions  have  been  drawn  from 
data  secured  in  field  experiments  with  soils,  which  it  is  hoped  may  be 
avoided  in  the  future  by  the  application  of  the  principles  herein 
outlined. 


1919]      W  ay  niclc- Sharp :  Variations  in  Nitrogen  and  Carbon  in  Field  Soils       139 


BIBLIOGRAPHY 

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Eeport  of  the  Committee  on  Standardization  of  Field  Experiments.  Jour. 
Amer.  Soc.  Agron.,  vol.  9,  pp.  402-409,  1917. 

2  Hibbard,  P.  L. 

Notes  on  the  Determination  of  Nitrogen  by  the  Kjeldahl  Method.  Jour.  Ind. 
and  Eng.  Chem.,  vol.  2,  pp.  463-466,  1910. 

s  Surface,  Frank  M.,  and  Pearl,  Eaymond. 

A  Method  of  Correcting  for  Soil  Heterogenity  in  Variety  Tests.  Jour.  Agr. 
Ees.,  vol.  V,  no.  22,  pp.  1039-1050,  1915. 

4  Waynick,  D.  D. 

A  Modification  of  the  Wet  Combustion  Method  for  Determining  Total  Carbon 
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s  Waynick,  D.  D, 

Variability  in  Soils  and  Its  Significance  to  Past  and  Future  Soil  Investiga- 
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